TY - JOUR
T1 - A power series method for solving initial value problems utilizing computer algebra systems
AU - Schovanec, Lawrence
AU - White, J. T.
N1 - Funding Information:
' Research supported by the Texas Advanced Research Program, under Grant No. 003644-101
PY - 1993/1/1
Y1 - 1993/1/1
N2 - This paper introduces an iterative method for generating the Taylor polynomial of the solution to an analytic initial value problem and is based upon the utilisation of a symbolic manipulation language. As developed here, the mth iterate of this procedure is precisely the mth degree Taylor polynomial of the solution. Error estimates are provided which are readily calculated with a computer algebra system. Examples are presented which illustrate the method and its ease of application.
AB - This paper introduces an iterative method for generating the Taylor polynomial of the solution to an analytic initial value problem and is based upon the utilisation of a symbolic manipulation language. As developed here, the mth iterate of this procedure is precisely the mth degree Taylor polynomial of the solution. Error estimates are provided which are readily calculated with a computer algebra system. Examples are presented which illustrate the method and its ease of application.
KW - Initial value problems
KW - symbolic manipulation
UR - http://www.scopus.com/inward/record.url?scp=84953466520&partnerID=8YFLogxK
U2 - 10.1080/00207169308804175
DO - 10.1080/00207169308804175
M3 - Article
AN - SCOPUS:84953466520
SN - 0020-7160
VL - 47
SP - 181
EP - 189
JO - International Journal of Computer Mathematics
JF - International Journal of Computer Mathematics
IS - 3-4
ER -